Anderson localization of cold atomic gases with effective spin-orbit interaction in a quasiperiodic optical lattice

We theoretically investigate the localization properties of a spin-orbit-coupled spin-1/2 particle moving in a one-dimensional quasiperiodic potential, which can be experimentally implemented using cold atoms trapped in a quasiperiodic optical lattice potential and external laser fields. We present the phase diagram in the parameter space of the disorder strength and those related to the spin-orbit coupling. The phase diagram is verified via multifractal analysis of the atomic wave functions and the numerical simulation of diffusion dynamics. We found that spin-orbit coupling can lead to spectra mixing (coexistence of extended and localized states) and the appearance of mobility edges.

Figure 1

Schematic diagram showing the system under consideration.

Figure 2

Phase diagram for Anderson localization of SO-coupled BEC in 1D quasiperiodic lattice in the parameter space $\Delta$-$\Omega$. $\gamma =0.7$, $\Delta$ and $\Omega$ are estimated in units of $J$.

Figure 3

Total bandwidth versus period $q$. At $q\to \infty$ the system becomes quasiperiodic. The parameters are specified in the figure.

Figure 4

Eigenenergies obtained from numerical diagonalization of Hamiltonian matrix, as a function of $\Delta /J$. Calculations are performed under periodic condition with $\beta =610/987$, $N=987$, $\gamma =0.7$ and (a) $\Omega =0.1$; (b) $\Omega =1$.

Figure 5

${\alpha }_{\min }$ versus $1/n$ for the wave functions of the lowest band $◯$ $\left(i=1\right)$ and the center band $\square$ $\left(i=F_n\right)$. (a) $\Omega /J=0.2$, $\Delta /J=1.5$; (b) $\Omega /J=0.4$, $\Delta /J=1.5$; and (c) $\Omega /J=2.5$, $\Delta /J=0.1$ correspond to extend phase, critical phase, and localize phase, respectively.

Figure 6

Time evolution of the wave packet width $w\left(t\right)$: (a) without SO interaction; (b) in the presence of SO interaction with $\gamma =0.7$ and $\Omega /J=0.2$.

Figure 7

Time evolution of wave packets $|{\psi }_{j,\uparrow }{|}^2$ corresponds to Fig. 6b at specific times.